Red Clay or Sandstone Veneer On Concrete Slab?

1945 home here in Tucson. My wife and I bought this house three years ago and she wants to ditch the carpet. I pulled up the carpet in the first room and discovered red floors. Looking closely where the tack strip nails chipped out the concrete, it's apparent that it's a thin red veneer (1/8" or less) on the concrete foundation. There's evidence of linoleum adhesive from some time in the past, and when I scraped and sanded at it, it came up very easily leaving lots of red dust.

So what is this red layer, exactly, and was it put there for functional or aesthetic purposes? We like the red brick-like color. If we want to leave it exposed, what would be the best process/product for sealing it? I'm thinking of patching and painting over the divots around the edge of the room. Will paint stick to it okay?